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A282107 Numbers n with k digits in base x (MSD(n)_x=d_k, LSD(n)_x=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 2. 18

%I

%S 5,7,10,14,17,20,21,27,28,31,34,35,39,40,42,49,54,56,57,62,65,68,70,

%T 73,78,80,84,85,93,98,99,107,108,112,114,119,124,127,130,133,136,140,

%U 141,146,147,155,156,160,161,167,168,170,175,177,186,196,198,201,214

%N Numbers n with k digits in base x (MSD(n)_x=d_k, LSD(n)_x=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 2.

%C All the palindromic numbers in base 2 with an odd number of digits belong to the sequence.

%C Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.

%H Paolo P. Lava, <a href="/A282107/b282107.txt">Table of n, a(n) for n = 1..10000</a>

%e 897 in base 2 is 1110000001. If j = 7 (the first 0 from left) we have 1*1 + 1*2 + 1*3 = 6 for the left side and 0*1 + 0*2 + 0*3 + 0*4 + 0*5 + 1*6 = 6 for the right one.

%p P:=proc(n,h) local a,j,k: a:=convert(n, base, h):

%p for k from 1 to nops(a)-1 do

%p if add(a[j]*(k-j),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a))

%p then RETURN(n); break: fi: od: end: seq(P(i,2),i=1..10^3);

%Y Cf. A282108 - A282115.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Feb 06 2017

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Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)